Towards the thermodynamics of localization processes

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In this article, the authors study the entropy time evolution of a quantum mechanical model, which is frequently used as a prototype for Anderson's localization.

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8 p.

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Grigolini, Paolo; Pala, Marco G.; Palatella, Luigi & Roncaglia, Roberto September 2000.

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In this article, the authors study the entropy time evolution of a quantum mechanical model, which is frequently used as a prototype for Anderson's localization.

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8 p.

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Copyright 2000 American Physical Society. The following article appeared in Physical Review E, 62:3, pp. 3429-3436; http://pre.aps.org/abstract/PRE/v62/i3/p3429_1

Abstract: We study the entropy time evolution of a quantum mechanical model, which is frequently used as a prototype for Anderson's localization. Recently Latora and Baranger found that there exist three entropy regimes, a transient regime of passage from dynamics to thermodynamics, a linear-in-time regime of entropy increase, that is, a thermodynamic regime of Kolmogorov kind, and a saturation regime. We use the nonextensive entropic indicator advocated by Tsallis with a mobile entropic index q, and we find that the adoption of the "magic" value q=Q=1/2, compared to the traditional entropic index q=1, reduces the length of the transient regime and makes earlier the emergence of the Kolmogorov regime. We adopt a two-site model to explain these properties by means of an analytical treatment and we argue that Q=1/2 might be a typical signature of the occurrence of Anderson localization.

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  • Physical Review E, 2000, College Park: American Physical Society, pp. 3429-3436

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  • Publication Title: Physical Review E
  • Volume: 62
  • Issue: 3
  • Page Start: 3429
  • Page End: 3436
  • Pages: 8
  • Peer Reviewed: Yes

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  • September 2000

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  • March 9, 2012, 2:17 p.m.

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  • April 1, 2014, 12:55 p.m.

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Grigolini, Paolo; Pala, Marco G.; Palatella, Luigi & Roncaglia, Roberto. Towards the thermodynamics of localization processes, article, September 2000; [College Park, Maryland]. (digital.library.unt.edu/ark:/67531/metadc77163/: accessed September 24, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT College of Arts and Sciences.